The real-time solution to a mathematical problem arises in numerous fields of science, engineering, and business. It is usually an essential part of many solutions, e.g., matrix/vector computation, optimization, control theory, kinematics, signal processing, andpattern recognition. In recent years, due to the in-depth research on neural networks, numerous recurrent neural networks (RNN) based on the gradient-based method have been developed and investigated. Particularly, some simple neural networks were proposed tosolve linear programming problems in real time and implemented on analog circuits. In this book, ZNN, ZD or ZND theory formalizes these problems and solutions in the time-varying context and provides compact models that could solve those dynamic problems.
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